If the Senate fails to reach an agreement, interest rates on new Stafford student loans will double from 3.4 to 6.8 percent. The doubling would affect the 7 million students who receive Stafford loans, which serve only the neediest of students.

Watch 2 Georgetown University students discuss their struggles with student loans HERE.

The Senate's effort to pass comprehensive immigration reform legislation, which is expected to be put to a vote by the end of this week, has consumed most of the bandwidth in the chamber.

"We're working right through immigration," said Senate Majority Leader Harry Reid, D-Nev. "We are going to wrap up immigration either Thursday or Friday. The only question now is whether we can come up with a list of amendments. And I think both sides want to do that, but having said that, I don't know we can do it."

"We probably can't get it done this week," said Sen. Tom Harkin, chairman of the Senate Health Education, Labor and Pensions Committee.

Harkin's original proposal, which was outvoted in the Senate, would keep rates at 3.4 percent for two years.

A bipartisan coalition of senators reportedly began working on a compromise last week which would link interest rates to financial markets and fix those rates for the life of the loan. The plan, developed in talks by Sen. Joe Manchin, D-W.Va., Sen. Tom Coburn, R-Okla., Sen. Angus King, I-Maine, and Sen. Lamar Alexander, R-Tenn., would leave rates at about 3.8 percent, according to the Associated Press. It would not include a cap on interest rates.

Manchin's office would not comment on the proposal, and King's spokesman Crystal Canney said only that they "are still working on it."

"If Republicans will agree to a cap, I think we can get this done in a heartbeat," added Harkin. "I've been working with Senator Alexander. We're pretty darn close-except for that sticking point of keeping the cap."

If there's no action on the bill, senators will depart for their July 4 recess, but could work on fixing the interest rates retroactively after they return. But a compromise isn't necessarily the best option, said Harkin.

"I have said all along that we need to keep interest rates at 3.4 percent. Extend it for at least another year,"said Harkin. "It needs to be decided within the framework of the overall Higher education. What are we going to do about college affordability, and transparency, and holding colleges accountable for outcomes and graduation rates? That's where this ought to be, not separated out individually."